What are the divisors of 5243?

1, 7, 49, 107, 749, 5243

There is a total of 6 positive divisors.
The sum of these divisors is 6156.
The arithmetic mean is 1026.

6 odd divisors

1, 7, 49, 107, 749, 5243

How to compute the divisors of 5243?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 5243 by each of the numbers from 1 to 5243 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

5243 / 1 = 5243 (the remainder is 0, so 1 is a divisor of 5243)
5243 / 2 = 2621.5 (the remainder is 1, so 2 is not a divisor of 5243)
5243 / 3 = 1747.6666666667 (the remainder is 2, so 3 is not a divisor of 5243)
...
5243 / 5242 = 1.0001907668829 (the remainder is 1, so 5242 is not a divisor of 5243)
5243 / 5243 = 1 (the remainder is 0, so 5243 is a divisor of 5243)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 5243 (i.e. 72.40856302952). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

5243 / 1 = 5243 (the remainder is 0, so 1 and 5243 are divisors of 5243)
5243 / 2 = 2621.5 (the remainder is 1, so 2 is not a divisor of 5243)
5243 / 3 = 1747.6666666667 (the remainder is 2, so 3 is not a divisor of 5243)
...
5243 / 71 = 73.845070422535 (the remainder is 60, so 71 is not a divisor of 5243)
5243 / 72 = 72.819444444444 (the remainder is 59, so 72 is not a divisor of 5243)